We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-3, author = {Janusz Gwo\'zdziewicz and Maciej S\k ekalski}, title = {A polynomial with 2k critical values at infinity}, journal = {Annales Polonici Mathematici}, volume = {83}, year = {2004}, pages = {41-44}, zbl = {1100.30002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-3} }
Janusz Gwoździewicz; Maciej Sękalski. A polynomial with 2k critical values at infinity. Annales Polonici Mathematici, Tome 83 (2004) pp. 41-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-3/